Blasting method

ABSTRACT

Methods for evaluating drill pattern parameters such as burden, spacing, borehole diameter, etc., at a blast site are disclosed. One method involves accumulating the burden contributed by successive layers of rock and matching the accumulated rock burden to a target value for a borehole having a length related to the average height of the layers. Another method relates to varying drill pattern parameters and characteristics to match blast design constraints, including the substitution of one explosive material for another by the proper balance of materials and/or output energies to the associated rock burden. Analysis of deviations from target rock burdens and corrective measures are disclosed, as well as cost optimization methods. The various methods can be practiced using an appropriately programmed general purpose computer.

RELATED APPLICATION

This application is a continuation application of application Ser. No.12/180,302 filed Jul. 25, 2008 now abandoned which is a divisional ofapplication Ser. No. 10/911,792 filed Aug. 3, 2004, now U.S. Pat.7,418,373, which is a divisional of application Ser. No. 09/391,831filed Sep. 8, 1999, now U.S. Pat. 6,772,105, each of which is herebyincorporated herein by reference in its entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention pertains to bench blasting methods and, in particular, toa method of selecting the placement of boreholes along a drill line.

In modern bench blasting, vertical or near vertical holes are drilledadjacent to a rock face and are loaded with explosive charges that arethen detonated. The detonation fractures the rock mass between theborehole and the rock face and displaces the resulting fractured rock.The resulting broken rock, known as “muck”, is removed and a new freerock face is thus exposed. If the muck contains a desired product, itcan be gathered and processed. Otherwise, it may simply be removed fromthe blasting site to permit further blasting or other activities.

2. Related Art

U.S. Pat. No. 3,377,909 to Grant et al, issued Apr. 16, 1968, disclosesthe use of a “powder factor” (cubic yards of earth per pound ofexplosive) to characterize a bore-hole pattern in a coal field stripmine and discloses a “normal” spacing for ANFO (see col. 7, lines 70-71and 6, lines 63-68).

U.S. Pat. No. 3,848,927 to Livingston, dated Nov. 19, 1974, discloses atrial and error method of determining the optimum and critical depths ofa small charge, and teaches the scaling-up of this information forlarger charges based on cube root scaling (see col. 7, lines 6-45). Thispatent suggests matching the charge to the desired size of debris.

U.S. Pat. No. 4,273,049 to Edwards et al, dated Jun. 16, 1981, suggestsover-coming the dampening effect of water in a borehole by usingwater-resistant explosive in the water-containing portions of theborehole and conventional explosives above those portions.

U.S. Pat. No. 4,440,447 to Ricketts et al, dated Apr. 3, 1984, teachesthat, in a borehole array for the formation of a retort in oil shale,outer boreholes can be closely spaced and made smaller in diameter tomaintain the powder factor (see col. 8, lines 40-53), which is definedas the ratio of energy or explosive used per unit volume of formationexplosively expanded in pounds ANFO equivalent per ton of oil shaleformation expanded (see column 10, lines 13-17). No explanation of theterm “ANFO equivalent” is given.

International Patent Application PCT/GB90/00567, which is incorporatedherein by reference or background information, discloses a laserrangefinder device referred to by the trademark QUARRYMAN that can beused to survey a rock face and, when given a borehole pattern by theuser, to calculate the burden associated with each borehole. This patentapplication also discloses a borehole analyzer referred to by thetrademark BORETRAK that allows the user to determine the configurationof a borehole as actually drilled.

Prior art methods for assessing the rock hole burden associated with agiven borehole or, alternatively, for predicting the optimum positionsfor boreholes along a rock face, made use only of gross approximationsof the burdens associated with the boreholes. Typically, the volume ofexplosive material in the borehole is calculated and a known conversionfactor corresponding to the powder factor disclosed in U.S. Pat. No.3,377,909 (discussed above) is used to project a volume of rock to beassociated with the explosive material in the borehole, i.e., the rockburden. The rock burden is then expressed as a roughly rectangularblock, one dimension of which corresponds to the length of the column ofexplosive material in the borehole, another to the distance of theborehole to the rock face. The projected hole spacing along the drillline can then be derived as the third dimension of the rectangularblock. This calculation method is highly inefficient because it does nottake into account significant variations in the configuration of therock face that can occur within the dimensions of the rectangular blockassociated with the borehole.

SUMMARY OF THE INVENTION

One broad aspect of the present invention pertains to a method forestablishing a drill pattern for a plurality of boreholes ofpredetermined diameter for use with a specified explosive material alonga drill line along a bench of rock having a known density and a rockface. The method comprises (a) defining a drill line having a startpoint and an end point; (b) determining a target rock burden B_(T) for ahypothetical borehole having the predetermined diameter at the startpoint; (c) defining along the drill line a progression of successivelayers of rock, each layer defining an incremental burden, anddetermining the cumulative burden B_(cum) of the successive layers andrevising B_(T) with each successive layer until B_(cum), accounts forone-half of B_(T); (d) setting and indicating a position for theborehole on the drill line in the most distant layer from the startpoint; (e) defining additional successive layers of rock until the totalof the incremental burdens of the layers defined in steps (c) and (e)accounts for B_(T); (f) setting and indicating a location for a distantboundary of the rock burden for the borehole; and (g) using the distantboundary as the start point for an additional bore-hole and repeatingsteps (b), (c) (d), (e) and (f) for each additional borehole until alayer coincides with the end point.

In one example, such a method may comprise the foregoing steps (a) and(b) and then (c) defining along the drill line a progression ofsuccessive intermediate layers of rock each having a mass less than thetarget rock burden B_(T) and being bounded by an intermediate boundaryplane and a distant boundary plane and for each intermediate layer (i)calculating a revised B_(T) based on a hypothetical borehole on the lastde-fined boundary plane, and (ii) determining the cumulative burdenB_(cum) of the defined incremental intermediate layers until B_(cum)accounts for one-half of B_(T) and then setting and indicating thelocation of a borehole on the drill line in the last defined layer(referred to as the “central layer”); (d) defining along the drill linea progression of successive distant layers of rock, and accumulating therock burdens of the layers until the total rock burden accumulated insteps (c) and (d) accounts for B_(T); (e) setting and indicating alocation for a distant boundary of the rock burden for the borehole; and(f) using the distant boundary as a start point and returning to steps(b)-(e) until an incremental layer coincides with the end point.

Optionally, the position of the borehole may be set between the planarboundaries of the central layer by interpolation or on one of theboundaries.

Another aspect of this invention relates to a method for proposing adrill pattern comprising positions for boreholes of predetermineddiameter for use with a specified explosive material along a drill linealong a bench of rock having a known density and rock face. The methodcomprises (a) defining a drill line having a start point and an endpoint; (b) determining a target rock burden (B_(T)) for a hypotheticalborehole having a height corresponding to the start point; (c) definingalong the drill line a progression of successive layers of rock eachhaving a mass less than B_(T) and each being bounded by planar crosssections of the bench and having an intermediate boundary plane and adistant boundary plane, determining the cumulative burden B_(cum) of thedefined layers, and calculating an average height of the layers witheach successive layer; (d) using the average height to calculate arevised B_(T) for the hypothetical borehole; and (e) repeating steps (c)and (d) until B_(cum) accounts for B_(T) and then indicating thelocation of a borehole on the drill line between the start point and themost distant layer, and using the distant boundary of the most distantlayer as a start point and returning to step (b) until a layer coincideswith the end point.

According to one aspect of the invention, calculating the average heightof the incremental layers may comprise defining spaced parallel planesthat define layer boundaries and taking the average height of theplanes.

According to another aspect of the invention, the rock mass of a layermay be calculated as the rock density multiplied by the volume of thelayer and the volume may be calculated as one-half of the sum of thesurface areas of the planes bounding the layer multiplied by the spacingbetween the planes.

According to still another aspect of the invention, determining B_(T)may comprise determining the amount of the specified explosive materialthat would be loaded in the hypothetical borehole, converting the amountto a corresponding quantity of a reference explosive material andcalculating a target burden associated with the corresponding quantityof the reference explosive material. Optionally, converting the amountto a corresponding quantity of a reference explosive material maycomprise scaling the mass of the specified explosive material by therelative magnitudes of the specific energies of the specified explosivematerial and the reference explosive material. In a particularembodiment, calculating the target burden may comprise determining aMaterial Factor for the reference explosive material and multiplying thecorresponding quantity by the Material Factor.

According to yet another aspect of the invention, determining B_(T) maycomprise determining an Energy Factor for the rock burden and relatingthe rock burden to the amount of explosive material that would be in thehypothetical borehole using the Energy Factor.

The method of this invention may optionally include designating blastdesign constraints comprising minimum and maximum values forhole-to-rock face burden, hole spacing and at least one of a MaterialFactor and Energy Factor and determining and indicating for eachborehole whether the constraints are met. Optionally, the drill patterncharacteristics of each borehole may be determined on asection-by-section basis for each borehole. The method may furtherinclude analyzing deviations of drill pattern characteristics from theconstraints to evaluate at least one of the drill line distance anddrill line orientation relative to the rock face and indicating theevaluation. Optionally, the method may include identifying and reportingeach borehole having an excess toe burden or a swell or a hollow in therock face.

The present invention further provides a method for determining apriority-directed loading configuration for a borehole subject to blastdesign criteria. This method comprises (a) selecting a segment of theexplosive column portion of the borehole to be filled with explosivematerial; (b) determining the rock burden associated with the identifiedsegment; (c) evaluating candidate explosive materials for use in theidentified segment in order of priority until one is found that meetsthe blast de-sign criteria (referred to herein as a compliant material),and assigning the first compliant material to the selected segment,assigning stemming to the segment when all the candidate explosivematerials fail to meet the minimum energy factor criterion andindicating “unknown” when all the candidate explosive materials exceedthe maximum energy factor criterion; and (d) repeating steps (a), (b)and (c) for each segment of the explosive column. Optionally, theexplosive materials may be evaluated in order of cost to generate acost-directed loading configuration. Alternatively, the explosivematerials may be evaluated in order of specific energy. In a particularembodiment, the method may comprise assigning stemming to the segmentwhen each evaluated explosive material provides less than a minimumenergy factor criterion for the rock burden. The method may optionallyfurther comprise indicating whether all candidate explosive materialsexceed the maximum energy criterion for a segment of the borehole.

The present invention also provides a method for choosing at least oneexplosive material for use in at least a segment of a borehole, themethod comprising determining a target specific volume energy requiredfor an explosive material in the borehole; and identifying at least oneexplosive material that provides at least the target specific volumeenergy. This method of the present invention may comprise comparing thespecific energies of candidate explosive materials to the targetspecific volume energy, which may optionally comprise referring tostored data that indicate specific volume energies of a plurality ofexplosive materials. The stored data may indicate the densities andspecific mass energies of the various candidate explosive materials, andidentifying an explosive material may comprise calculating the specificvolume energy of a candidate explosive material and comparing thecandidate specific volume energy to the target specific volume energy.

Optionally, the method may comprise partitioning the borehole intosegments and determining rock burden and target specific volume energyfor various segments of the borehole and separately identifying anexplosive material for each segment. In a particular embodiment, themethod may further comprise determining the rock burden for the boreholeand using a predetermined Energy Factor and the size of the borehole todetermine the corresponding specific volume energy.

Another method of the present invention relates to evaluating thesuitability of a candidate explosive material of known specific energyfor use in at least a segment of a borehole having a predetermineddiameter and having a rock burden associated therewith by identifying areference Material Factor (MF_(R)) for the rock burden associated withthe borehole with reference to a reference explosive material of knownspecific energy; calculating an adjusted Material Factor (MF_(A))corresponding to the use of the candidate explosive material in theborehole; and comparing the adjusted Material Factor (MF_(A)) to thereference Material Factor (MF_(R)). Calculating the adjusted MaterialFactor (MF_(A)) may comprise multiplying the reference Material Factor(MF_(R)) by (M_(Ref))(E_(Ref))/(M_(EXP))(B_(EXP)); wherein M_(Ref)=themass of reference explosive in the section of the borehole; M_(EXP)=themass of candidate explosive in the section of the borehole; E_(ref)=thespecific mass energy of the reference explosive; and E_(EXP)=thespecific mass energy of the candidate explosive, so thatMF_(A)=MF_(R)((M_(Ref))(E_(Ref))/(M_(EXP))(E_(EXP))).

The present invention also provides a method for selecting the diameterof a borehole by (a) determining the rock burden associated with atleast a segment of the borehole; (b) determining a target Energy FactorEF_(T) for the rock burden; (c) selecting an explosive material of knownspecific volume energy; and (d) calculating the diameter of the boreholeneeded to accommodate a volume of the explosive material sufficient toattain at least the target Energy Factor EF_(T).

The present invention further provides a computer-readable medium havingcomputer-executable code therein for assigning positions for boreholesof predetermined diameter for use with a specified explosive materialalong a primary drill line along a bench of rock having a known densityand having a rock face. Such a medium comprises (a) code responsive touser input defining a drill line having a start point and an end point;(b) code for determining a target rock burden B_(T) for a hypotheticalborehole having a height corresponding to the start point; (c) coderesponsive to data reflecting a model of the bench for defining alongthe drill line an incremental layer of rock having a mass less thanB_(T) and having an intermediate boundary and a distant boundary,determining the cumulative burden B_(cum) of the defined incrementallayers, and the height of the layer at the distant boundary; (d) codefor using the height at the distant boundary to calculate a revisedB_(T); (e) code for causing the further execution of code (c) and code(d) until B_(cum) accounts for one-half B_(T); (t) code for setting andindicating the location of a borehole on the drill line between theintermediate boundary and the distant boundary of the last incrementallayer when B_(cum) accounts for B_(T); (g) code responsive to said datafor defining along the drill line further incremental layers of rockuntil B_(cum) accounts for B_(T); and (h) code for setting andindicating the position of the distant boundary of the rock burdenassociated with the borehole, and until the position of any previouslyaccumulated layer exceeds the end point, for using the distant boundaryof the rock burden as a start point and repeating the code of parts(b)-(g).

Further still, this invention relates to a computer-readable mediumcomprising (a) code responsive to user input defining a drill linehaving a start point and an end point; (b) code for determining a targetrock burden B_(T) based on a hypothetical bore-hole having thepredetermined diameter at the start point; (c) code responsive to datareflecting a model of the bench, for defining along the drill line aprogression of successive intermediate layers of rock each having a massless than the target rock burden B_(T) and being bounded by anintermediate boundary plane and a distant boundary plane and for eachproximal layer (i) calculating a revised B_(T) based on a hypotheticalborehole on the last defined distant boundary plane and (ii) determiningthe cumulative burden B_(cum) of the defined intermediate until B_(cum)accounts for about one-half of B_(T) and then setting and indicating thelocation of a borehole on the drill line in the last defined layer(referred to as the “central layer”); (d) code for defining along thedrill line a progression of successive distant layers of rock, andaccumulating the rock burdens of the distant layers until the total rockburden accumulated in steps (c) and (d) accounts for about B_(T); (e)code for setting and indicating the distant boundary of the rock burdenfor the borehole; and (f) code for using the distant boundary as a startpoint and repeating steps (b)-(e) until an incremental layer coincideswith the end point.

The medium may optionally further comprise code for determining theposition of the borehole between said intermediate and distantboundaries by interpolation.

In an alternative embodiment, the medium may comprise (a) coderesponsive to user input defining a drill line having a start point andan end point; (b) code for determining a target rock burden (B_(T)) fora hypothetical borehole having a height corresponding to the startpoint; (c) code responsive to data reflecting a model of the bench fordefining along the drill line an incremental layer of rock having a massless than B_(T) and having a distant boundary, determining thecumulative burden (B_(cum)) of the defined incremental layers, andcalculating an average height of the incremental layers with eachsuccessive layer; (d) code for using each average height to calculate arevised B_(T) for the hypothetical borehole; (e) code for comparingB_(cum) to B_(T) for each successive layer and then for causing thefurther execution of code (c) and code (d) if B_(cum) is less thanB_(T); (f) code for setting and indicating the location of a borehole onthe drill line between the intermediate boundary and the distantboundary of the last incremental layer when B_(cum) is not less thanB_(T), and using the distant boundary of the last incremental layer as astart point in response to code (e) when B_(cum) is not less than B_(T);and (g) code for comparing each incremental layer to the end point andfor causing the execution of code (b)-(e) until an incremental layercoincides with the end point.

Optionally, the code (c) for calculating the average height of theincremental layers may comprise code for defining spaced parallel planesthat define layer boundaries and taking the average height of theplanes. Also, the code (c) for determining B_(cum) may include code forcalculating the volume of the layer as one-half of the sum of thesurface areas of the planes bounding the layer multiplied by the spacingbetween the planes, and for calculating the rock mass by multiplying therock density by the volume. The code (d) may include code fordetermining the amount of the specified explosive material that would beloaded in the hypothetical borehole, determining the quantity of areference explosive material corresponding to the calculated volume of aspecified explosive material and calculating a target burden associatedwith the corresponding quantity of the reference explosive material. Themedium may comprise code for scaling a mass of a specified explosivematerial by the relative magnitudes of the specific energies of thespecified explosive material and the reference explosive material. Codefor calculating the target burden may comprise code for determining aMass Factor for the reference explosive material and multiplying thecorresponding quantity by the Mass Factor.

The medium may comprise code for determining B_(T) by determining anEnergy Factor for the rock burden and relating the rock burden to theamount of explosive material that would be in the hypothetical boreholeusing the Energy Factor.

There may also be code in the medium for designating blast designconstraints comprising minimum and maximum values for hole-to-rock faceburden, hole spacing and at least one of a Material Factor and EnergyFactor, and for determining the drill pattern characteristics of eachborehole and comparing the characteristics to the constraints andindicating whether the constraints are met. Optionally, there may becode for determining the drill pattern characteristics of each boreholeon a section-by-section basis for each borehole. There may also be codefor analyzing deviations of drill pattern characteristics from theconstraints to evaluate at least one of the drill line distance anddrill line orientation relative to the rock face and reporting theevaluation. Optionally, the medium may comprise code for identifying andreporting each borehole having an excess toe burden, and/or a swell orhollow in the rock face.

The invention also provides a computer-readable medium havingcomputer-readable code therein for choosing at least one explosivematerial for use in at least a segment of a borehole having a rockburden associated therewith, comprising code for determining a targetspecific volume energy required for an explosive material relative tothe associated rock burden; and code for identifying at least oneexplosive material that provides at least the target specific volumeenergy. Such medium may comprise code for referring to stored dataindicating the specific energies of candidate explosive materials andcomparing the data to the target specific volume energy. The data mayindicate the specific volume energies of a plurality of blends of two ormore materials. Alternatively, the medium may comprise data indicatingthe densities and specific mass energies of the various candidateexplosive materials, and may comprise code for calculating the specificvolume energy of a candidate explosive material and comparing thecandidate specific volume energy to the target specific volume energy.Optionally, the medium may comprise code for partitioning the boreholeinto segments and determining rock burden and target specific volumeenergy for various segments of the borehole and separately identifyingan explosive material for each segment. There may be code fordetermining the rock burden for the borehole and using a pre-determinedEnergy Factor and the size of the borehole to determine the requiredspecific volume energy.

Still another aspect of this invention relates to a computer-readablemedium having computer-readable code therein for evaluating thesuitability of a candidate explosive material of known specific energyfor use in at least a segment of a borehole having a predetermineddiameter and having a rock burden associated therewith, the codecomprising code responsive to data indicating the specific energy ofreference explosive material and a target rock burden to determine areference Material Factor (MF_(R)) for the rock burden associated withthe borehole; code responsive to data for a candidate explosive materialfor calculating an adjusted Material Factor (MF_(A)) corresponding tothe use of the candidate explosive material in the borehole; and codefor comparing the adjusted Material Factor (MF_(A)) to the referenceMaterial Factor (MF_(R)) and for indicating the result. The medium maycomprise code for calculating the adjusted Material Factor (MF_(A)) bymultiplying the reference Material Factor (MF_(R)) by(M_(Ref))(E_(Ref))/(M_(EXP))(E_(EXP)); wherein M_(Ref)=the mass ofreference explosive in the section of the borehole; M_(EXP)=the mass ofcandidate explosive in the section of the borehole; E_(Ref)=the specificmass energy of the reference explosive; and E_(EXP)=the specific massenergy of the candidate explosive material.

Further still, the present invention provides a computer-readable mediumhaving a computer-executable code therein for selecting the diameter ofa borehole, the code comprising (a) code for accepting rock burden dataassociated with at least a segment of the borehole; (b) code foraccepting a target Energy Factor for the rock burden EF_(T); (c) codefor accessing data pertaining to the specific energy of an explosivematerial; and (d) code for calculating the diameter of the boreholeneeded to accommodate a volume of the explosive material sufficient toattain the target Energy Factor EF_(T).

The present invention further relates to a method for using a computerto assign positions for boreholes at a bench blasting site having a rockface, comprising inputting data indicating bench characteristicsindicating at least bench height, bank angle, rock face configurationand rock density; inputting blast design constraints pertaining tospacing, hole-to-rock face burden, explosive material properties,desired borehole angle, at least one of Material Factor and EnergyFactor; inputting a proposed drill line, start point and end point; andreceiving a report containing proposed drill pattern characteristics.

In one embodiment of the invention, the report may identify boreholeshaving excess toe burdens and the method may further comprise inputtingdata indicating the placement of boreholes in the toe and receiving areport indicating positions for boreholes on the drill line. Optionally,the report may identify boreholes having rock face swells and the methodmay comprise inputting data indicating the elimination of at least oneborehole position and the addition of at least one borehole on a swellbetween the drill line and the rock face.

Another method aspect of this invention relates to a method forassigning a cost-directed spacing to a borehole of predetermineddiameter on a drill line along a bench of rock having a known densityand a rock face, each location and borehole being subject to blastdesign criteria including a minimum spacing criterion, a maximum spacingcriterion, and a minimum energy factor. The method comprises (i)proposing a compliant spacing for a borehole on the drill line withreference to at least one associated burden boundary; (ii) associatingwith the borehole a rock burden determined in part relative to the atleast one burden boundary; (iii) determining a cost-based loadingconfiguration for the borehole according to the method described aboveand recording the resulting compliant configuration (if any) anddetermining its associated cost; (iv) proposing a different compliantspacing with a corresponding borehole-boundary distance; (v) repeatingstep (ii), (iii) and (iv) for each different compliant spacing; and (vi)identifying the compliant spacing with the lowest cost (on a dollar perton basis) compliant loading configuration (referred to as thecost-directed spacing). Step (vi) may optionally comprise identifyingthe location of the borehole and of the first and second boundaries ofthe rock burden associated with the cost-directed spacing. The methodmay optionally be repeated by using a boundary associated with thecost-directed spacing as a fixed boundary for the rock burden of asubsequent borehole on the drill line to assign a cost-directed spacingto the subsequent borehole. In one embodiment, the method may comprisefirst proposing in step (i) a spacing that corresponds to the minimumspacing criterion and proposing in step (iv) an incrementally largerspacing than was used in the previous steps (ii) and (iii).Alternatively, the method may comprise proposing in step (ii) a spacingthat corresponds to the maximum spacing criterion and proposing in step(iv) an incrementally smaller spacing than was used in the previoussteps (ii) and (iii).

This invention also provides a computer-readable medium havingcomputer-executable code therein, comprising (a) code for selecting asegment of the explosive column portion of a borehole to be filled withexplosive material; (b) code for determining the rock burden associatedwith the selected segment and for accessing data pertaining to blastdesign criteria comprising minimum and maximum energy factors and foraccessing data pertaining to candidate explosive materials; (c) code forevaluating candidate explosive materials for use in the selected segmentin order of priority until one is found that meets the blast designcriteria (referred to herein as a compliant material), and for assigningthe first compliant material to the selected segment, for assigningstemming to the segment when all candidate explosive materials fail tomeet the minimum energy factor criterion, and for indicating whether allthe candidate explosive materials exceed the maximum energy factorcriterion; and (d) code that causes code (a), (b) and (c) to repeat foreach segment of the explosive column. Optionally, there may be code forevaluating explosive materials in order of cost to generate acost-directed loading configuration. There may be code for evaluatingexplosive materials in order of specific energy.

The invention further provides a computer-readable medium havingcomputer-executable code therein for assigning a cost-directed spacingto a borehole of predetermined diameter on a drill line along a bench ofrock having a known density and a rock face, the spacing and boreholebeing subject to blast design criteria including minimum spacing,maximum spacing, and minimum and maximum energy factors, the mediumcomprising (i) code for accessing data relating to the configuration ofa bench and to blast design criteria comprising minimum and maximumenergy factors and data comprising energy and cost characteristics ofcandidate explosive materials; (ii) code responsive to user inputdefining on the bench a drill line having a drill line start point and adrill line end point; (iii) code for proposing a compliant spacing for aborehole on the drill line with reference to at least one burdenboundary; (iv) code for associating with the borehole a rock burdendetermined in part relative to the at least one burden boundary; (v)code for determining a cost-based loading configuration for the boreholeas described herein and for indicating the resulting compliantconfiguration (if any) and determining its associated cost; (vi) codefor proposing a different compliant spacing with a correspondingborehole-boundary distance and for causing code (iv) and (v) to repeatfor each different compliant spacing; and (vii) code for indicating thecompliant spacing with the lowest cost (on a dollar per ton basis)compliant loading configuration (referred to as the cost-directedspacing). The medium may optionally comprise code for indicating thelocation of the borehole and of the first and second boundaries of therock burden associated with the cost-directed spacing. Also optionally,the medium may comprise code for using a boundary associated with thecost-directed spacing as a boundary for the rock burden of a subsequentborehole on the drill line and executing the code of parts (iii)-(vii)to assign a cost-directed spacing to the subsequent borehole.

The invention also provides apparatuses for assigning positions forboreholes of predetermined diameter for use with a specified explosivematerial along a primary drill line along a bench of rock having a knowndensity and a rock face. The invention also provides apparatuses forchoosing at least one explosive material for use in at least one segmentof a borehole having a rock burden associated therewith, and apparatusesfor selecting the diameter of a borehole. Each such apparatus comprisesa computer processor; storage media accessible to the processor, forstoring data and executable code; input means for delivering data to theat least one storage medium as described above; and output means forconveying data representing locations for boreholes, identifying anexplosive material for use in a borehole segment and/or representing aselected diameter for a borehole, as appropriate.

The method of this invention may provide for reducing the cost of ablast pattern by (a) broadening at least one constraint by an acceptabledegree to yield revised constraints; (b) proposing a hole position at aminimum spacing constraint; (c) evaluating a hole at that position forcompliance with the revised constraints and calculating and recordingthe cost per unit burden mass for blasting at that position; (d)proposing another position for the hole at a different compliantspacing; (e) repeating steps (c) and (d) until the constraints are nolonger met, then (f) evaluating the calculated costs per unit burdenmass and indicating the spacing having the lowest cost per unit burdenmass. The method may optionally include (g) proposing the next boreholeat the minimum spacing from the previous hole; and (h) repeating theevaluation of steps (c)-(g) until the end point is reached.

Inputting data for the practice of any invention disclosed herein maycomprise retrieving data from a memory medium, transferring data from anelectronic surveying device, and/or entering data via a user inputdevice. Setting data may comprise determining its value, e.g., setting aposition or location for a borehole or boundary comprises determining,e.g., by approximate calculation, the proper position or location.Indicating data, such as the output of a computer program representing alocation or position or the result of a comparison between two or moregiven values, may comprise displaying the data, recording the data forfuture retrieval and/or sending the data to another electronic device.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a perspective view of a bench to be blasted, showing variouscharacteristics of the bench and the boreholes therein;

FIG. 2 is a schematic representation of a computer system suitable forthe practice of the present invention;

FIG. 3A is a partly cross-sectional, perspective volumetric view of abench to be blasted using boreholes placed in accordance with the priorart;

FIG. 3B is a partly cross-sectional, perspective volumetric view of abench to be blasted using boreholes placed in accordance with thepresent invention.

FIG. 4 is a schematic cross-sectional view of boreholes along a drillline angled with respect to a rock face;

FIG. 5 is a schematic plan view of a bench having a swell in front of adrill line and additional boreholes in the swell, between the drill lineand the rock face;

FIG. 6 is a schematic cross-sectional view of a bench taken along aplane through a borehole in the bench;

FIG. 7 is a plot of a specific energy vs. blend ratio for blends of ANFOand an emulsion-type explosive material;

FIG. 8A is a schematic plan view of a bench having an excess toe burden;

FIG. 8B is a schematic cross-sectional view of the bench of FIG. 8Ataken along line B-B;

FIG. 9 is a flow chart illustrating the method for identifying acost-directed spacing for at least one borehole on a drill line inaccordance with one aspect of the present invention;

FIG. 10A is a schematic cross-sectional representation of the boreholeplanned at the 12-foot spacing in Example 7 with the height andthickness of the bench indicated in feet on the vertical and horizontalaxes;

FIG. 10B is a burden chart pertaining to the cross section of FIG. 10A,indicating hole depth on the vertical axis and hole-to-rock face burdenon the horizontal axis;

FIG. 11A is a schematic cross-sectional representation of the boreholeplanned at the 15-foot spacing of Example 7 with the height andthickness of the bench indicated in feet on the vertical and horizontalaxes; and

FIG. 11B is a burden chart pertaining to the cross section of FIG. 11A,indicating hole depth on the vertical axis and hole-to-rock face burdenon the horizontal axis.

DETAILED DESCRIPTION OF THE INVENTION AND PREFERRED EMBODIMENTS THEREOF

The present invention provides a method and apparatus for determiningthe optimum placement of boreholes along a drill line for a rock face.The invention permits the use of, and may be embodied as improvementsto, prior art devices such as the QUARRYMAN® and BORETRAK® systems whichpreviously merely facilitated a trial-and-error assessment of boreholepatterns chosen by the user. Such prior art devices had no provisiontherein to suggest to the user the appropriate positions for boreholesbased on selected parameters pertaining to the blast site as provided bythe invention described herein.

The present invention provides a significant improvement to prior artpractice by providing an iterative method for assessing the rock burdenassociated with a borehole. As a result of the use of this method, whichis described more fully below, the rock burden associated with aparticular borehole is very closely matched to the explosive materialplanned for use in the borehole. Accordingly, burden-related factorssuch as rock size distribution can be carefully controlled so thatinadequate use and/or excessive use of explosive material can be avoidedto a degree not realized in prior art practice.

In accordance with one embodiment of the present invention, the usergenerates a model of a bench to be blasted; this may be a numeric modelproduced by an electronic surveying device such as the QUARRYMAN®device. The user selects a drill line and indicates a boundary thereonto delineate the start of the blast area, the boundary providing a startpoint for the analysis. The model is used to calculate thecross-sectional area of the bench at the start point as the area of afirst plane disposed perpendicular to the drill line. The height of thefirst plane at the drill line is determined and is used to establish ahypothetical height for a borehole and, therefore, a hypotheticalloading of explosive. A layer of rock is defined between the firstplanar cross section of the bench and a second plane parallel to thefirst, the horizontal (top) and vertical faces of the rock face, groundlevel at the bottom of the borehole and a planar boundary through thedrill line at an angle corresponding to the borehole angle, or atanother angle designated by the user. The thickness of the layer alongthe drill line is chosen so that the volume of rock therein is expectedto be significantly less than the target burden to be associated withthe hypothetical borehole, typically not more than twenty percentthereof, preferably about ten percent of the target burden.Alternatively, the thickness of the layers is chosen to be aboutone-tenth of the desired minimum spacing for the blast. A thickness oftwo feet is suitable as a default. The layer is thus bounded by twoparallel planes that are preferably disposed perpendicularly to thedrill line: an intermediate boundary plane and a distant boundary plane,the terms “intermediate” and “distant” indicating their relativeproximity to the start point. The height of the distant boundary planeat the drill line is used to calculate a length for the hypotheticalborehole and the amount of explosive therein and the target burden B_(T)for the borehole are then recalculated using the revised boreholelength. The incremental burden associated with the layer is calculatedand compared to the target burden. If the incremental burden is lessthan one-half of the target burden, another layer is added by defininganother plane parallel to the last and the height of the new plane isused to calculate a revised length for the hypothetical borehole and thetarget burden for the borehole is again recalculated. With each addedlayer, the incremental burdens of the previously defined layers areadded together and compared to the target burden for the borehole asmost recently revised. As long as the accumulated burden is less thanone-half of the target burden, an additional layer is added and therecalculation of the target burden based on the revised height of theborehole is performed. When the accumulated burden “accounts for”, i.e.,substantially meets (e.g., is within about 1% of the accumulatedburden), or exceeds, one-half of the target burden, the position of theborehole is set within the last defined layer. The layers between thestart point and the borehole are referred to as “intermediate” layers.Preferably, the position of the borehole within the last defined layeris fixed by interpolation to identify the position on the drill line atwhich the accumulated burden of the intermediate layers preciselymatches or at least more closely approximates the target burden. Oncethe borehole position is set, a first boundary plane through theborehole location is defined and additional layers, referred to as“distant layers”, are added and their incremental burdens areaccumulated without revising the length or target burden of theborehole. When the total accumulated burden of the intermediate burdenlayers and the distant burden layers accounts for, i.e., meets orexceeds, the target burden for the borehole, the distant boundary of therock burden for that borehole is set. Preferably, the position of thedistant boundary is determined by interpolation to identify the positionat which the total accumulated burden matches or closely approximatesthe target burden for the borehole. Optionally, once the position of theborehole has been set, the previously accumulated burden of theintermediate burden layers may be cleared and the burdens of the distantlayers may be accumulated until the total distant burden likewiseaccounts for one-half of the target burden for the borehole.Alternatively, the incremental burdens of the distant layers can beadded to the accumulated burdens of the intermediate layers until B_(T)is accounted for. In any of the foregoing approaches, the methodcomprises accumulating incremental burdens along the rock face beginningat a start point until about one-half of the target burden (the“intermediate half” of the target burden) is accounted for, and thenadding burdens of incremental layers on the “distant” side of theborehole until the other half of the target burden (the “distant half”of the target burden) is accounted for. Once the distant boundary of therock burden for a borehole is set, the distant boundary is used as astart point for positioning the next borehole and subsequent layers aremeasured therefrom. The procedure is repeated until the end point is metor exceeded.

In an alternative embodiment, the average of the heights of thecross-sectional planes is calculated and is used to calculate a revisedlength for the hypothetical borehole and amount of explosive therein,and the target burden B_(T) for the borehole is re-calculated. One byone, additional layers are defined by additional planes and areassociated with the hypothetical borehole. The burden contributed byeach layer (the “incremental burden”) is determined and is added to theincremental burdens associated with any previously defined layers andthe sum, i.e., the accumulated burden, is compared to the target burdenfor the hypothetical borehole. If the accumulated burden is less thanthe target burden, another layer is defined and the average height ofthe planes is recalculated and the borehole length and explosive loadingtherein is revised with each additional layer. When the accumulatedburden matches the target burden associated with the hypotheticalborehole, the position of the borehole is determined between theintermediate boundary and the distant boundary of the last defined layerand the method can be re-initiated to determine the best position forthe next borehole. The resulting drill pattern is evaluated with regardto predetermined blast constraints, e.g., minimum and maximum values forhole-to-rock face burden (“B”), hole spacing (“S”), uniformity, etc.,and adjustments are made where necessary to conform the drill pattern tothe constraints.

After the boreholes have been drilled in the positions specifiedaccording to the method described herein, they may be surveyed using adevice such as the BORE-TRAK® system. Such hole-surveying devices allowthe user to determine the degree to which the borehole, as drilled, hasdeviated from the planned position. For example, a borehole that wasintended to be perfectly vertical may have veered off in one directionor another. The BORETRAK® system allows the user to determine the actualconfiguration of the borehole. Then, the present invention provides amethod by which deviations in the burden associated with the boreholeresulting from the non-ideal configuration of the borehole can beaccounted for. In accordance with the present invention, a borehole canbe analyzed on a section-by-section basis to determine the rock burdenassociated with each segment. The present invention then provides thatan explosive material having sufficient output energy to accommodate theburden associated with a given section of borehole can be loaded intothat section. In this way, drilling deviations that would otherwise leadto burden-associated anomalies, such as inappropriate rock sizedistributions, can be ameliorated by the blast operator, thus keepingpost-blast operations running smoothly.

Another aspect of the present invention relates to the Applicant'srealization that a target rock burden for a borehole in a predetermineddrilling pattern for use with a specified explosive material can berelated to the explosive material on a scaleable basis that allows theuser to vary or revise the drilling parameters (borehole diameter,spacing, hole-to-rock face burden, etc.), including the choice ofexplosive material, to obtain successful outcomes without undueexperimentation. The scaled relationship between rock burden andexplosive material is referred to herein as the Material Factor and isabbreviated “MF”, and can be expressed in, and converted among,analogous expressions such as the “volume MF” (mass of rock (rockburden) per unit volume of explosive material) or “mass MF” (rock burdenper unit mass of explosive material). By determining mass MF or volumeMF that yield successful blast results for a given blast site andexplosive material, blast design criteria (such as borehole diameter,spacing and hole-to-rock face burden) can be varied and comparableresults can be obtained by maintaining the appropriate MF. For example,a target mass MF of 2.5 tons per pound explosive may have been derivedfrom previous success in the use of a drilling pattern where thehole-to-hole spacing S=13 feet and the front burden B=16 feet. If it isdesired to reduce 13 to 14 feet, this change may be accommodated bychanging the other blast site criteria to maintain the mass MF in thedesired range, e.g., by increasing 5 to 14.86 (=13×16/14) where theheight and diameter of the borehole are unchanged. Typical burdensassociated with the use of 94% ammonium nitrate and 6% fuel oil(ANFO)-loaded boreholes translate to a mass MF of from about 0.8 to 3.5tons of rock per pound ANFO. Since ANFO is so well-known and economical,and since successful blast site criteria have been established for ANFO,ANFO is referred to herein as a “known” explosive material and it isoften the starting or reference material for planning a blast patternand for evaluating reference Material Factors in accordance with themethod of the present invention. However, any known explosive materialmay serve as a reference material in the manner described herein.

According to one aspect of this invention, appropriate blast patterncriteria can be forecast for an unknown or “substitute” explosivematerial by relating the amount of substitute material to acorresponding quantity of a known explosive material by reference to thespecific energy of each material. The term “specific energy” refers to arelationship between a quantity of explosive material and the explosiveenergy it releases. Specific energy may be expressed in terms of energyper quantity (either mass or volume) of explosive material. Unlessotherwise stated, the term “specific energy” encompasses energy per unitmass of explosive material (e.g., calories per gram (cal/g)) and/orenergy per volume of explosive material (e.g., cal/cc). These may bedifferentiated as “specific mass energy” and “specific volume energy”,respectively. For example, ANFO is known to have a specific mass energyof 880 calories per gram (880 cal/g), equivalently stated as 400kcal/lb; 722 cal/cc and 2.045 kcal/cubic foot. The relation of aquantity of a substitute explosive material to a corresponding quantityof a known material can be achieved by multiplying the quantity ofsubstitute explosive material by the relative specific energies of thesubstitute and the known explosive materials. Emulsion-type explosivematerials, which are well-known in the art, may be used as substitutesfor ANFO, as may blends of ANFO with an emulsion. For example, to planfor the use of 45 pounds of a substitute explosive material “G” in placeof standard ANFO, e.g., an ANFO-emulsion blend having a specific massenergy of 760 cal/g (=3.45×10⁵ cal/lb), the 45 pounds of G is related toa corresponding quantity of ANFO of about 39 pounds as follows:

45 lbs “G”×(3.45×10⁵ cal/lb “G”)/(4×10⁵ cal/lb ANFO)=38.9 lbs ANFO. Theblast site criteria can then be established as if the load of explosivematerial was 39 pounds of ANFO, e.g., by employing a previously known MEfor ANFO.

According to still another aspect of the present invention, the energyreleased by an explosive material can be related directly to a burden tobe blasted. This allows flexible planning of blast site criteria forknown explosive material and allows predictable substitutions forexplosive materials. According to this aspect of the invention, the massof rock associated with a quantity of a known explosive material toyield a suitable MF can be related to the energy released by theexplosive material. This relationship is referred to herein as theEnergy Factor (“EF”). For example, a Material Factor of MF=2.5 tons rockper pound ANFO can be translated to an Energy Factor EF of (2.5 tonsrock/lb)×(2000 lbs per ton)×(1/(4×10⁵ cal/lb))=0.0125 lbs rock/cal. TheApplicant has realized that drill pattern criteria, including theexplosive material to be used, can be changed from an approvedconfiguration and acceptable results can be expected as long as theEnergy Factor is maintained at an appropriate value.

The use of Energy Factor as a blast criterion simplifies the evaluationof drill pattern parameters since it allows for consistency in resultswithout requiring that a quantity of one explosive material be expressedas a corresponding quantity of another material.

One strategy for using the Energy Factor EF is to specify a boreholepattern (i.e., the spacing, hole-to-rock face burden, and explosivecolumn diameter and height), calculate the rock burden associated with aborehole and then, based on a previously determined Energy Factor EF,determine the amount of energy required to successfully blast that rockburden. The required quantity of any explosive material whose specificenergy is known can then be determined. The borehole can be sized toaccommodate the required quantity of explosive material. Conversely, ifthe borehole size is predetermined, the other drill patternspecifications can be adjusted and/or an explosive material can beselected so that the EF for the site is within the desired value.

The invention will be understood in greater detail by reference to thefollowing Examples, which make reference to the Figures. FIG. 1 providesa perspective view of the rock face and indicates various benchcharacteristics and drill pattern characteristics that are relevant tothe present invention as well as to the prior art. For example, FIG. 1indicates bench characteristics such as bench height (also known as“face height”) 10, floor or final grade 12, toe 14, the crest 16, andbank angle 18, and drill pattern characteristics such as boreholediameter 20, hole depth 22, explosive column height 24, stem height 26,subgrade or subdrilling 28, spacing (“S”) 30 from one hole to the nexton a drill line, back break 32, side break 34, burden (“B”,“hole-to-rock face” burden or “front burden”) 36, bottom hole burden 38,burden (drill line-to-drill line burden) 40, drill line 42, start point44 and end point 46. Material Factors and Energy Factors are also drillpattern characteristics. It will be noted that the term “burden” is usedin the art in several senses. To avoid confusion herein, the term“hole-to-rock face burden” (B—a distance) shall refer to the distancefrom the borehole to the crest of the rock face and the term “rockburden” (B_(T)—a volume) shall indicate the amount of material to beblasted by a given hole. Other senses of the term “burden” will beapparent from the context of use.

It will be understood that the methods described herein can beimplemented as a computer program that can receive blast site data fromuser inputs and from devices such as the QUARRYMAN® and BORETRAK®systems and that can be configured to produce a variety of reportspresenting the end result of the various calculations described above. Aprogrammer of ordinary skill in the art will be able to create apro-gram to perform the functions described herein without undueexperimentation. FIG. 2 shows a general purpose computer system 50comprising a video display 52 (which may optionally comprise atouch-sensitive or light-sensitive screen and thus constitute a combinedinput/output device), a computer unit 54 that comprises a centralprocessing unit (CPU) 62 and a variety of conventional storage media onwhich a computer program and related data for practicing this inventioncan be recorded and accessed by the CPU. Such storage media arewell-known in the art; typical examples are an internal hard drive 54 a,read only memory (ROM) 54 b (which may be provided in any of a varietyof ROM types known in the art, e.g., PROM, EPROM, etc.), random accessmemory (RAM) 54 c, a “floppy” disc drive 54 d for utilizing a floppydisc 54 e, a compact disc (CD) drive 54 f for utilizing a CD 54 g, etc.The system 50 includes user input devices including a keyboard inputdevice 56, microphone 57 and a mouse input device 58, and output devicessuch as a printer 60, the display 52, and one or more audio speakers 52a. Components such as modems, communication ports (e.g., comm port 54h), touch screens, disc drives, etc., can be also used as input devicesto provide data to the computer. FIG. 2 also indicates that computersystem 50 can be connected in a conventional manner to a surveyingdevice 64 such as the QUARRYMAN® device referred to herein to providedata comprising a digitized model of the bench and rock face.

EXAMPLE 1 Prior Art

In a typical prior art procedure alluded to above, a rock face issurveyed using laser rangefinding equipment such as the commerciallyavailable QUARRYMAN® device. Next, rock face profiling software such asFACE 3-D® software available from Blast Design International, Inc. or asimilar software program can be used to produce a three-dimensionalmodel of the rock face, from which isometric, plan and cross-sectionalviews may be constructed. FIG. 3A shows the computer model of the rockface in front of a planned drill line A-B as generated by the FACE 3-D®soft-ware.

Once the rock face has been surveyed, the computer model generated bythe software may be used to evaluate borehole positions, spacings,angles, and to calculate the explosive energy distribution throughoutthe rock mass on a hole-by-hole basis for specified explosives. In aparticular example, a drill line A-B indicated in FIG. 3A and a seriesof seven boreholes 66 a, 66 b, . . . 66 g along the drill line isproposed by the user, based on past experience. The user also indicatesthe depth of stemming planned for each borehole, the density of the rockand other blast site criteria. The FACE 3-D® software uses theinformation provided by the user and can report the expected burdenassociated with each borehole. The mass of rock associated with a givenlength of explosive column (L), i.e., the “rock burden”, may becalculated as follows:M _(rock) =V×? _(R)  (1)whereV=B×L×S  (2)where M_(rock)=the mass of rock; V=the volume of rock; ?_(R)=the densityof the rock; and where B=hole-to-rock face burden; L=length of explosivecolumn; S=spacing between adjacent boreholes. The results can becompared against a target rock burden for the given volume of explosive.The FACE 3-D® software also provides a calculation of the burden atvarious depths along a borehole, based on cross sections of the rockface taken at positions along the drill line that correspond to boreholesites. Accordingly, the FACE 3-D® software will produce a cross sectionof the bench taken along a plane 68 a that is perpendicular to drillline A-B. Plane 68 a is bounded by the top surface of the bench, thebank face, the floor or final grade of the blast site and the boreholeitself.

A sample drill pattern analysis representative of a FACE 3-D®-typeproduct of the prior art is set forth in the following TABLE I for theseven holes indicated in FIG. 3A.

TABLE I Details Of Intended Boreholes (All angles in degrees. Allmeasurements in feet.) Holes Drilled to 498.0 Elevation at 15° angleMinimum Average Hole-to- Hole-to- Hole Distance Hole (Sub Bench RockFace Rock Face No. Along AB Depth Drill) Height Burden Burden 66a 20.085.0 0.8 81.3 14.2 16.5 66b 37.0 84.5 1.2 80.4 12.3 15.4 66c 54.0 82.51.6 78.4 13.5 15.6 66d 71.0 82.0 1.1 78.0 15.0 16.2 66e 88.0 80.5 1.975.9 14.7 16.8 66f 105.0 79.5 2.3 74.6 13.4 17.5 66g 122.0 78.5 2.2 73.519.4 26.5

If the user determines that any of the data of TABLE I show that theplanned drilling pattern produces a rock burden that is outside of thedesired limitations, the user can change one or more drill patterncriteria such as hole spacing and obtain a revised analysis. Althoughthis method is more accurate than other prior art methods fordetermining rock burdens, the calculations performed by the FACE 3-D®software give at best a rough indication of the actual rock burdenassociated with a borehole, so the outcome must be viewed withreservations even when it is favorable.

EXAMPLE 2A

One example of a procedure in accordance with the present invention maybe based on the following blasting site characteristics:

Face Height (FH) at start point=80 feet

Desired Stein Height (SH)=10 feet

Subdrilling (SD)=5 feet

Bore Hole diameter (d)=6.5 inches (16.5 centimeters (cm))

Explosive=ANFO

(Density(ANFO)(?_(EXP))=0.82 g/cm³; Specific Energy (ANFO)=880 cal/g)

Desired MF=3 tons rock per pound ANFO

Rock density (?_(R))=2.25 tons/yd³

The optimum positions for boreholes along a selected drill line toachieve proper fragmentation are determined as follows, with referenceto FIG. 3B, which represents a portion of the same bench shown in FIG.3A.

1. The bench, including the rock face, is electronically surveyed andmodeled, preferably with optional discount for the presence of residualdebris (“muck”) that may have been interpreted as solid rock. Whenmodeling is done by digital surveying methods, e.g., by use of theQUARRYMAN® system, the muck can be discounted for by adjusting thespatial coordinates that made the base of the rock face.

2. Blast design parameters such as minimum and maximum boreholespacings, hole angles, hole-to-rock face burdens, explosive properties,rock properties, desired Material Factors and/or Energy Factors areestablished.

3. The desired drill line and a start point A (FIG. 3B) and end point Bthereon are specified.

4. The given borehole diameter is attributed to a hypothetical verticalborehole located at the start point, at which point the borehole isattributed an explosive column length of 75 feet (calculated as thebench height (80 feet) less the planned stem height (10 feet) plus theplanned sub-drilling (5 feet)). The resulting hypothetical volume ofexplosive material is about 17.3 ft³. This corresponds to 4.019×10⁵ g(about 885.2 lbs) of ANFO. Given the Material Factor MF of 3 tons rockper pound ANFO, the initial target rock burden (B_(T)) for thishypothetical borehole is (3)×(885.2)=2655.6 tons rock or 1180.3 cubicyards rock.

5. The area of a cross section, e.g., cross section Ca-1, of the benchat the start point is calculated and a similar area is calculated for asecond cross section Ca-2 parallel to the first at an incrementaldistance of e.g., 2 feet, along the drill line towards the desiredlocation for the next borehole.

6. The volume of rock between the cross sections, referred to herein asa “layer” of the rock face, e.g., layer La-1, is calculated bymultiplying the distance between the cross sections (i.e., the thicknessof the layer) times the average of the areas of the two adjacent crosssections that define the layer.

7. The length of the hypothetical borehole and the hypothetical volumeof explosive therein are revised based on the height of the last definedplane at the drill line, and the target rock burden is recalculated,based on the revised hypothetical borehole length and desired MF.

8. The mass of rock in the layer is added to all previously definedlayers defined from the start point (if any) and the accumulated rockmass is compared to the target rock burden B_(T).

9. If the accumulated rock mass is less than one-half of the revisedtarget rock burden, another cross section, e.g., cross section Ca-3, andanother layer, e.g., layer La-2, are defined and steps 6, 7 and 8 arerepeated. In this way, the length, volume and B_(T) of the hypotheticalborehole are updated. When the accumulated rock mass of the definedlayers La-1, La-2, etc., reaches or exceeds one-half of the updatedB_(T), the position of the borehole along the drill line is set in thelast defined layer, e.g., on or between the intermediate and distantboundary planes of the last layer, e.g., at 66 a′ (on the distantboundary). Additional layers are defined, one by one, until the totalaccumulated burden is not less than B_(T) for the borehole. The distantboundary plane 66 ax of the last defined layer is the distant boundaryfor the burden associated with borehole 66 a′ and is used to establish astart point and the process is re-initiated to deter-mine the placementof the next borehole. This process assures that the quantity ofexplosive material in the boreholes is closely matched to the rockburdens associated therewith, and that no layer of rock is associatedwith more than one borehole. Accordingly, the method of the presentinvention indicates the placement of boreholes in a manner that helpsassure a uniform energy distribution from the explosive material intothe surrounding rock.

EXAMPLE 2B

An alternative procedure, described herein with reference to FIG. 3B,follows the steps of Example 2A except that instead of steps 7, 8 and 9of Example 2A, the following steps 7′, 8′ and 9′ are preferred:

7′. The length of the hypothetical borehole and the hypothetical volumeof explosive therein are revised based on the average of the heights ofthe defined cross sections, and the target rock burden B_(T) isrecalculated, based on the revised hypothetical borehole height anddesired MF.

8′. The mass of rock in the layer is added to all previously definedlayers defined from the start point (if any) and the accumulated rockmass is compared to the target rock burden.

9′. If the accumulated rock mass is less than the revised B_(T), anothercross section and layer are defined and steps 6, 7′ and 8′ are repeated.In this way, the length and volume of the hypothetical borehole and theassociated target rock burden are updated on an iterative basis based onthe average heights of all of the defined layers. When the accumulatedrock mass of the defined layers reaches or exceeds the updated B_(T),the position of the borehole 66 a′ along the drill line is specified ashalf-way between the start point and the distant boundary plane of thelast defined cross section. The distant boundary plane of the lastdefined layer is then used as a new start point and the process isre-initiated to determine the placement of the next borehole. Thisprocess assures that the quantity of explosive material in the boreholesis closely matched to the rock burdens associated therewith, and that nolayer of rock is associated with more than one borehole. Accordingly,the method of the present invention indicates the placement of boreholesin a manner that helps assure a uniform energy distribution from theexplosive material into the surrounding rock.

EXAMPLE 3A

This Example provides an extension of the method of Examples 2A or 2Bfor further improving the drill pattern characteristics at the blastsite. Once the borehole positions are indicated by the process describedin Example 2A or 2B, face profiles, i.e., cross-sectional planes, arecharacterized for the borehole positions. The hole-to-rock face burden,Material Factor and/or Energy Factor and hole spacing characteristicsare calculated for each borehole on a section-by-section basis and arecompared against the earlier designated drill pattern or “blast design”constraints. If the blast design constraints have been met consistently,the user may be provided the option of optimizing the cost of the blastas described in Example 3B. If the constraints are not met, an analysisis performed to determined how the deviations can be addressed.

In the event that blast constraints have not been consistently met, thedrill pattern characteristic can be analyzed to determine whether achange in the position and/or orientation of the drill line wouldresolve the deviation. For example, the drill pattern characteristicsmay be examined to see whether the hole-to-rock face burdens wereconsistently low. If so, the planned position for the drill line may bemoved away from the rock face and the iterative calculations of Example2A or 2B will be repeated to determine new borehole locations. If thehole-to-rock face burdens are consistently high, the drill line may bemoved closer to the rock face and the iterative calculations of Example2A or 2B are repeated to determine new borehole locations. If thehole-to-rock face burdens are not consistently low or high, thedeviations are examined to see whether a trend indicates that the drillline is improperly disposed at an angle relative to the rock face, assuggested in FIG. 4. If so, the drill line can be re-oriented and theprocess of Example 2A or 2B repeated. An angled drill line orientationcan be discerned from changes in the ratio of hole spacings tohole-to-rock face burdens for the holes on the drill line.

If the deviations cannot be resolved by moving or re-orienting the drillline, the drill pattern characteristics are examined to determinewhether rock face irregularities are causing the deviations. In one modeof analysis, the hole-to-rock face burden is calculated at variouspoints along each borehole to determine whether there are significantvariations along the length of the borehole. If the rock face is roughlyparallel to the borehole, the hole-to-rock face burdens should be nearlyuniform along the length of each borehole even when there is adifference in burden from one borehole to the next. In such case, therock face may have a swell (as suggested in FIG. 5) or a trough. In thecase of a swell, the process of Example 2A or 2B would result in aseries of boreholes situated close together to offset the increasedhole-to-rock face burden. In such case, alternate holes on the drillline (X₁, X₂, . . . ) may be eliminated while additional holes (Y₁, Z₁,. . . ) are added between the drill line and the rock face. The drillpattern characteristics (e.g., hole locations, burdens, spacing,Material Factor and/or Energy Factors) are recalculated and comparedagain to the blast constraints. If necessary, further holes can beeliminated and/or additional holes (Y₂, Z₂, . . . ) can be situated inthe swell region between the drill line and the rock face, as indicatedin FIG. 5, until the drill pattern characteristics are within thedesignated constraints. Conversely, if the rock face has a trough(concave region) relative to the drill line, the calculations of Example2A or 2B will result in widely spaced boreholes along the trough. Insuch case, additional boreholes may be added, and/or the hole diametersmay be modified, so that maximum spacing constraints are not exceededand the drill line may then be moved away from the rock face so that thehole-to-rock face burdens in the concave region meet the blast designconstraints. The non-concave regions may then have excessive MaterialFactors but this may be reduced by adding holes between the drill lineand the rock face in the same manner as for swells.

Once a drill pattern in which all blast design constraints are met hasbeen established, the actual loading of explosive materials in the holespositioned according to that pattern is determined by examining planarcross sections near and in front of each hole location, andrecalculating the drill pattern characteristics to confirm that theblast pattern criteria, especially the MF and/or EF, have been met.Preferably, the drill pattern characteristics and, optionally, thecalculations leading thereto are presented to the user as an output.

EXAMPLE 3B

Cost Reduction

The present invention includes a cost reduction procedure which mayoptionally be used in situations where borehole burdens are not uniformfrom segment to segment in a borehole even though the drill patternsatisfies the designated blast design criteria. According to thisprocedure, at least one blast design constraint, e.g., MF, is relaxed.For example, a range of acceptable MF of 1.0 to 2.6 may be specifiedinstead of a particular target value of 2.5. Alternatively, a specifictarget spacing may be relaxed to allow for spacings that provide aspacing-to-burden (hole-to-rock face burden) in the range of 0.75:1 to2:1. A hole is hypothetically designated at a minimum allowable spacingfrom the preceding hole. (The first hole is designated at one-half theminimum spacing, measured from the start point.) The loading ofexplosive material that would go in the hole is calculated based onplanar cross sections of the rock face through and near the hole. Thehole is then analyzed to determine whether blasting constraints (e.g.,MF) have been met. If so, the cost for filling the hole with theexplosive material is calculated and recorded, optionally in terms ofdollars per ton of rock burden associated with the hole (dollar burden).The hole spacing may then be increased incrementally (e.g., in 1-footincrements) and the suggested loading and resulting drill patterncharacteristics recalculated and compared again to the constraints. Theprocess is repeated until at least one blast design characteristic failsto meet the blast design constraints. At that point, the previouslyproposed costs are compared and the hole providing the lowest dollarburden is identified. The next hole is then initially positioned at theminimum allowable spacing and the process is repeated until the minimumcost is attained for each hole. At the end of the process, a reportindicating the positions of minimum dollar burden and their blast designcharacteristics may be generated.

EXAMPLE 4

This example illustrates the method described above for accommodatingthe use of substitute explosive materials at the blast site.

As indicated above, the specific output energy of ANFO is known to be880 cal/g. When ANFO, which has a density of 0.82 g/cc (51.17 lb/ft³),is loaded in a borehole having a diameter d of 6.75 inches (17.145 cm),the volume of a three-foot section of the borehole is 3ft×(1/2)(3.145)(6.75 in/12 in/ft)²=0.7455 cubic feet=2.11×10⁴ cc; whichcorresponds to about 38.1 pounds ANFO. Suppose that the target rockburden for a three-foot length of the borehole is 72.45 tons of rock. Inaccordance with the present invention, the target burden is related tothe charge of ANFO to establish a Material Factor (MF) for the blastsite. In this case, the ANFO MF=72.45/38.1=1.9 tons rock per pound ANFO.

A substitute for standard ANFO, e.g., a mixture of ANFO and an emulsionexplosive, having a density ? of 1.17 g/cc and a specific output energyof 812 cal/g, may be accommodated as follows.

A. Retaining borehole size; adjusting the borehole positions toaccommodate a substitute explosive material.

The quantity of substitute explosive “S” in the three-foot section ofthe borehole is M=V?=(2.11×10⁴ cc)×(1.17 g/cc)=2.47×10⁴ grams. Given thespecific energy of 812 cal/g for the substitute material, the totaloutput energy for this volume of substitute explosive is (2.47×10⁴g)×(812 cal/g)=2004×10⁴ calories. The hypothetical quantity of ANFO thatwould give the same total output energy is (2004×10⁴ cal)/(880cal/g)=22,779 grams or 50.17 pounds ANFO. Using the Material Factor forANFO given above, the burden for the borehole using the substituteexplosive should be 1.9 tons rock per pound ANFO×50.17 pounds=95.3 tons.The drill pattern criteria should be adjusted, e.g., by increasing oneor both of the hole spacing, the hole-to-rock face burden, etc., toprovide for this increased rock burden.

In an alternative approach, the specific energies of ANFO and of thesubstitute material can be used to provide a scaling factor, as follows.When filled with the substitute material, the borehole segment willcontain (0.7455 ft³)×(1.17 g/cc)×(1/454 g/lb)×(30.48 cc/ft³)=54.4 poundsof substitute explosive material. The corresponding weight of ANFO maybe determined by multiplying the mass of substitute explosive (54 lbs)by the scaling factor defined as the specific energy of the substitutematerial divided by the specific energy of reference material (ANFO), asfollows. 54.4 lb “S”×(812 cal/g “S”)/(880 cal/g ANFO)=50.2 lbs ANFO.Given the target MF for ANFO of 1.9, the rock burden associated with thesubstitute explosive in the borehole should be (1.9)(50.2)=95.38 tons.The drill pattern may then be modified to provide this rock burden forthe borehole.

B. Maintaining the borehole positions (i.e., the rock burden)

(i). Adjusting borehole size to a substitute explosive material.

If the borehole positions are maintained, the rock burden associatedtherewith will be constant. Changing the explosive material maytherefore require changing the size of the borehole if the EF (orcorresponding MF) is to be maintained. One way to determine the sizeappropriate for the substitute material in accordance with the presentinvention is to re-size the borehole to accommodate sufficientsubstitute explosive material to substantially maintain the EnergyFactor EF in the desired range.

As indicated above, the Material Factor MF was given at 1.9 tons rockper pound ANFO. The corresponding Energy Factor EF is (1.9)×(2000lb/ton)×(1/454 g/lb)×(1/880 cal/g)=0.0116 pounds rock per calorie. The72.45 tons of rock associated with a borehole therefore requires (72.45tons)×(2000 lb/ton)×(1/0.0116 pound/cal)=1.25×10⁷ cal for properfragmentation. The quantity of substitute material required to providethis much energy at 812 cal/g is 15,383.5 grams, which corresponds to avolume of 13,150 cc=0.465 ft³. To provide this volume in the three-footsection of the borehole, the diameter d would have to bed=[0.465×(1/3.1415)]^(1/2)=0.385 ft=4.62 inches.

(ii). Choosing an alternate explosive material when borehole positionsand sizes are fixed.

Suppose a borehole is drilled and, because of deviation from thedrilling, the target MF of 1.9 tons rock per pound ANFO is exceededsignificantly in a particular 3-foot segment having a rock burden of75.45 tons associated therewith, e.g., the MF turns out to be 2.4. Asubstitute explosive can be identified as follows. Determine the EnergyFactor corresponding to the target MF as well as the amount of energythat would be released by ANFO at the target rock burden for thatthree-foot section of borehole. For example, (75.45 tons rock)/(19 tonsrock/lb ANFO)×(454 g/lb)×(880 cal/g)=0.587×10⁷ cal would be released byANFO in that segment of the borehole. The volume of substitute materialthat would fill the 3-foot section of borehole is determined and thecorresponding specific volume energy needed to blast the rock burden isfound. By referring to stored data of explosive materials, a substitutematerial having the needed specific energy can be identified.

EXAMPLE 5

This Example illustrates how the present invention can be used todetermine the loading of various explosive materials in a borehole. FIG.6 represents a cross section of a rock face taken along a borehole 18 ata blast site. The borehole is drilled at an angle of about 15 degreesfrom vertical. Surveying equipment such as the QUARRYMAN® system may beused to calculate the hole-to-rock face burden and rock burden for3-foot segments of the borehole. (The rock burden associated with asegment of a borehole may be described as the mass of rock in theportion of the bench whose height and position correspond to thelocation of the borehole segment and whose top and bottom surfaces areparallel to each other and horizontal and whose side surfaces aredefined by the rock face, the cross-sections of the bench at the startpoint and the stop point associated with the borehole (i.e., at theburden boundaries) and by a plane at the drill line and at the holeangle. As an optional alternative, an iterative, layer-by-layer methodfor determining the burden as described herein can be used.) The data ofTABLE II show the hole-to-rock face burden for the various segments andtheir associated Material Factor. It was established by the user thatthe Material Factor for this blast should be between 2 and 3 tons rockper pound ANFO.

TABLE II Burdens at Various Depths: Borehole of FIG. 6 ANFO Hole-to-RockMF Point Depth Face Burden ANFO (feet) (feet) (feet) (Actual) 1 0 18.5**** 2 3 **** **** 3 6 17.7 **** 4 9 17.9 **** 5 12 19.3 2.14 6 15 21.82.41 7 18 23.6 2.8  8 21 24.4 2.7  9 24 25.1 2.78 10 27 25.5 2.82 11 3024.8 2.74 12 33 24.2 2.68 13 36 24.9 2.75 14 39 26.5 2.92 SUBSTITUTEEXPLOSIVE MF Hole-to-Rock ANFO Point Depth Face Burden SCALED (feet)(feet) (feet) (Equivalent) 15 42 28   2.38 16 45 27.7 2.36 17 48 28.62.44 18 51 29.5 2.51 19 54 28.4 2.42 20 57 28.1 2.4  21 60 27.9 2.37 2263 28.2 2.4  23 66 28.4 2.42 24 69 27.8 2.37 25 72 28.2 2.4  26 75 28.72.44 27 78.1 28.9 2.46

It can be seen from TABLE II that the hole-to-rock face burden generallyincreases with the depth of the borehole (except at the 11-13 footrange), suggesting an increase in rock burden as well. AcceptableMaterial Factors were achieved for ANFO to a depth of about 40 feet(measuring points 1-14). Beyond that depth, the rock burden andtherefore the Material Factor became excessive in relation to ANFO andanother explosive material (an emulsion-type material) was evaluated.Scaled Material Factors were calculated based on the known density andspecific energy of the substitute material, and the results are setforth in TABLE II in connection with measuring points 15 through 27. Asseen from TABLE II, by employing the substitute explosive material, theScaled Material Factor was maintained within the desired range. Thisexample illustrates a method for the use of substitute materials toassure proper fragmentation even when burdens vary within a borehole toa degree that a reference explosive material would not functionadequately.

The selection and distribution of explosive materials and stemming in aborehole is referred to herein as the “loading configuration” of theborehole. If a loading configuration permits the borehole to satisfy theblast design criteria, the loading con-figuration is referred to as “acompliant loading configuration”.

The various explosive materials that are considered for use in theborehole, e.g., the reference material and the acceptable substitutestherefor, are sometimes referred to herein as “candidate explosivematerials”. In a computerized embodiment of this invention, the computersystem will include a database of candidate explosive materials andassociated pertinent data such as cost, density, specific energy, etc.The use of stemming may be indicated for a segment of a borehole forwhich all of the candidate materials appear to be excessively energetic,i.e., for which all candidate materials do not meet the minimum energyfactor criterion assigned to the borehole. On the other hand, if eventhe most highly energetic candidate explosive material fails to complywith the maximum energy factor criterion, the system can so indicate.For example, the system may generate a message that the appropriatematerial is “un-known”, i.e., that no satisfactory material is includedin the database.

Generally, this method may be referred to as a priority-directed loadingevaluation and it may comprise considering candidate materials in orderof any pertinent characteristics. In a priority-directed loadingevaluation, materials may be prioritized in order of sensitivity,stability, or any other pertinent characteristic, and are evaluated foruse in the borehole or in a segment of the borehole in order of theirpriority. The first compliant loading configuration generated therefrommay be referred to as the priority-directed loading configuration. Inreferring to particular embodiments of the method, the prioritycharacteristic is specifically identified, so the method can be referredto by replacing the term “priority” with the characteristic of interest.Thus, the evaluation of the candidate explosive materials in order ofcost per unit mass is referred to herein as a “cost-directedevaluation”, and the first compliant loading configuration generatedtherefrom is referred to herein as the “cost-directed loadingcon-figuration”. The evaluation of candidate materials in order ofstability would be referred to as a “stability-directed loadingevaluation” and the first compliant loading configuration generatedtherefrom would be identified as a “stability-based loadingconfiguration”. Other priority-directed loading evaluations and theinitial compliant loading configurations produced therefrom would besimilarly named. It should be noted that a priority-directed loadingevaluation does not include relocating the borehole on the drill line.

EXAMPLE 6

This Example illustrates how the procedures of the present invention canbe used to attain a desired Energy Factor in a blast hole through theuse of mixtures of two or more explosive materials, given a desiredMaterial Factor based on ANFO. To illustrate this embodiment, we shalluse the following criteria.

Rock Density ?=2.23 tons per yd³=0.0826 tons per ft³

Material Factor MF=2.5 tons rock per pound ANFO (per 553.66 cc ANFO)

Hole-to-rock face burden B=14 ft

Hole Spacing S=16 ft

Borehole Diameter d=4.5 inches=0.375 ft=11.43 cm

Borehole Segment L=1 ft=30.48 cm

Given the criteria listed above, the rock burden associated with theone-foot length L of the borehole is calculated as (1 ft)×(14 ft)×(16ft)×(0.0826 tons/ft3)=18.5 tons.

The volume of explosive material in the one-foot length of borehole is0.1104 ft³=3078.44 cc. Given the density of ANFO at 0.82 g/cc, thequantity of ANFO in the 1-foot borehole segment will be 2566.5 g (=5.65lbs). This translates to an MF of (18.5/5.56)=3.18 tons rock per poundANFO, a figure that exceeds the target MF and that indicates that ANFOwould be insufficient to produce the blasting results desired, using thegiven blast site criteria. To achieve the desired MF, it will thereforebe necessary either to use a greater quantity of ANFO or to use anexplosive with a greater specific volume energy than ANFO. To identifythe required material, it is necessary to determine the amount of energythat must be provided by the explosive material in that segment of theborehole.

As calculated above, the target MF would require 7.4 lbs ANFO which,given the specific energy of ANFO of 880 cal/g, (399,520 cal/lb), wouldprovide (7.4 lbs)×(399,520 cal/lb)=2,956,448 cal. This is the outputenergy that must be provided by the explosive material in the 1-footsegment of the borehole (3078.44 cc) to attain an Energy Factor thatwould result from the desired Material Factor of 2,5. For the materialin the one-foot segment of the borehole, this corresponds to a specificvolume energy of 960.4 cal/cc.

Having determined the specific volume energy required, a suitableexplosive material can be chosen. FIG. 7 provides data in the form of achart showing the relation between energy per unit volume (i.e.,specific volume energy) and composition for typical blends of emulsionexplosive and ANFO; such data can be provided in digital form for usewhen the foregoing procedure is performed on a computer.

Each part of the borehole can be analyzed in this way so that theexplosive materials therein provide a uniform Energy Factor throughoutthe rock face to accommodate for variations in burden along the lengthof the borehole as may occur with a bench having an excess toe burden assuggested in FIGS. 8A and 8B.

When a number of explosive materials are suitable, it may be desirableto refer to data indicating the costs of the materials and to indicatethose that provide the desired output energy for the lowest cost.

EXAMPLE 7

Another aspect of the present invention relates to generating a seriesof compliant, cost-directed loading configurations of a borehole in acycle of iterations of the method in Example 5 for various possiblespacings for the borehole from the burden boundaries, and identifyingthe spacing with the most cost-effective compliant loadingconfiguration. That borehole spacing is referred to herein as thecost-directed spacing. The method of this aspect of the invention isrepresented in flow chart form in FIG. 9, and the following descriptionof the method will relate to the flow chart. The method may beimplemented as a computer program by one of ordinary skill in the artand may be provided as a module available with the other computerizedmethods described herein. This method may optionally be used inconjunction with the method described in Example 3B.

First, the blast design constraints including minimum and maximum holespacing, minimum and maximum Energy Factors, stemming depth fromsurface, hole configuration (i.e., hole diameter, drilling angle, etc.),and a selection of candidate explosive materials are determined and, ina computerized embodiment of the invention, data relating thereto areentered into the computer (steps 110 and 112). The design criteriainclude pertinent characteristics of the candidate explosive materials,including cost, density and specific energy.

Before the first iteration, a borehole counter is initialized (step114). The cost-directed evaluation according to this method thencomprises proposing a compliant spacing for a borehole on the drill linewith reference to at least one associated burden boundary (step 116). Byproposing a compliant spacing, relative positions of the borehole and atleast one burden boundary are established on the drill line at a mutualdistance of one-half of the proposed spacing from the borehole. The rockburden on one side of the borehole between the borehole and the burdenboundary is then associated with the borehole. A like burden on theother side of the borehole is also associated with the borehole and isdefined by a boundary at a like distance from the borehole, i.e., thatthe borehole is at the linear center of the associated rock burden. Inthe case of the first borehole, proposing a compliant spacing maycomprise setting the position of the borehole (typically but optionallyat the start point of the drill line) and then setting a first boundaryfor the rock burden to be associated with the borehole at a distancealong the drill line of one-half of the proposed spacing, as in steps116 a, 116 b. Since the rock burden on the side of the borehole oppositethe first boundary may be undefined (e.g., the bench may not have beensurveyed in that direction), it may be assumed that the burdenassociated with the first borehole is the same on both sides of theborehole. Alternatively, the first boundary of the first borehole may beset on the drill line, e.g., at the start point. Proposing a spacing forthe first borehole is then like proposing a spacing for a subsequentborehole: the first boundary is deemed to be fixed in position on thedrill line and the borehole is set at a distance from the first boreholecorresponding to one-half of a compliant spacing. A second boundary isset at a like distance on the other side of the borehole (FIG. 9, step116 c). The burden associated with the borehole would then be defined bythe two boundaries and the borehole will be situated at the linearcenter between the boundaries. A cost-directed loading evaluation isthen performed, as shown in Example 5 (step 118). If a compliantcost-directed loading configuration is found, and the borehole meets theblast design criteria (query 120), the pertinent descriptive data areindicated, e.g., displayed, reported and/or recorded (step 122),preferably including a dollar-per-burden ton cost assessment of it. Theborehole-boundary spacing is then changed (step 124). In the case of afirst borehole in which the position of the borehole is fixed, this maymean moving at least one boundary relative to the borehole while keepingthe borehole set in place on the drill line. Otherwise, this may meanmoving the borehole and the second boundary relative to the firstboundary. In the case of a subsequent borehole, the first boundary willcoincide with the distant or second boundary of the previous borehole.The increment of the spacing preferably corresponds to the width of alayer of the bench, as described above. If the resulting spacing doesnot exceed either the minimum or the maximum allowable spacing criteriaand does not position the borehole beyond the end of the drill line(queries 126 and 128), another iteration of the cost-directed loadingevaluation is performed for the borehole with the new spacing (step118). The potential spacing is incremented and iterations are performeduntil an incremented location exceeds the end of the drill line (atwhich point the evaluation cycle is complete) or one of the spacingcriteria (queries 126 and 128). Otherwise, the process is stopped (step138). A cycle of this method will thus typically generate a series ofloading configurations for various potential spacings for the borehole,and will have recorded the associated cost and other descriptive datapertaining thereto. It will be understood that the order in whichspacings are evaluated is not critical to the practice of this method.Preferably, however, the first proposed spacing corresponds either tothe minimum or the maximum spacing criterion and each change in spacingis an incremental increase or decrease towards the other criterion.

If there were no spacings with compliant loading configurations (query130), an error message is indicated and the procedure is stopped (step132). If there was one or more spacings having a cost-directed loadingconfiguration, the spacing with the lowest dollar-per-ton cost, i.e.,the cost-directed spacing, is indicated, preferably with locations ofthe borehole and the burden boundaries of the associated burden (process134). Preferably, the pertinent cost data of the indicated borehole areindicated as well. Indicating data may comprise sending or displayingthe data to an output device or recording the data for later retrieval.Optionally, data pertaining to non-compliant configurations may berecorded for comparison to the data for compliant loadingconfigurations. The borehole counter may be incremented (step 136) andanother cycle of iterations may be initiated to evaluate possiblelocations for a subsequent borehole on the drill line. For a subsequentborehole, the distant boundary of the previous borehole at itscost-directed spacing is taken as the fixed first boundary of thesubsequent borehole. In this manner, the boreholes may be locatedsequentially at cost-directed spacings.

A particular example of the cost optimization routine described abovemay be as follows. In accordance with this example, which is based on amodel of a particular bench, the blast design criteria for this exampleare as follows:

-   -   Minimum Energy Factor=1.2    -   Maximum Energy Factor=2.5    -   Hole Diameter=6.75 inches    -   Stemming=9 feet    -   Sub-Drill=2 feet    -   Minimum Borehole Spacing=12 feet.

The first potential spacing for the borehole on the drill line is set atsix feet (one-half the minimum spacing) from the first burden boundary.A borehole at this first location would be characterized as follows:bench height—79.23 feet; hole depth—82.65 feet; azimuth—0.00; drillangle—12 degrees; vertical depth—80.84. The rock burden associated withthis borehole at the 12 foot spacing is 1,317 tons. FIG. 10A provides across-sectional representation of the bench and borehole at the firstspacing. FIG. 10B provides a representation of the hole-to-rock facerock burden associated with the borehole and indicates the depth ofloading of explosive and stemming.

The fixed costs associated with the borehole relate to the use of twocast boosters and two in-hole delay units. Other possible fixed costsmay obtain as well, e.g., the accessory cost (booster, delay units,etc.), drilling cost, an allocated portion of the blast design cost,etc., for a total of, e.g., $811.75. (All dollar figures presentedherein are provided for illustration purposes only.) The variable costassociated with the borehole relates primarily to the quantity and typeof explosive material used. In the present Example, ANFO is currentlythe least expensive and coincidentally the least energetic candidateexplosive material, and so is the first to be considered. The cost ofstemming is considered to be negligible in all cases.

The first iteration of the analysis of the borehole at the 12 footspacing does not yield a compliant loading configuration because whenthe minimum desired energy factor is satisfied, the ANFO is loaded inthe borehole from the depth of 82.65 feet to only 41 feet, so that thestemming exceeds the stated 9 feet criterion. The iteration can bestopped at this point because the other available explosive materialsare more energetic than ANFO and would generate similarly unacceptableresults. The variable cost for this loading configuration is the cost offilling 41.65 feet of the bore-hole with ANFO ($56.75).

In two subsequent iterations of the method described above, spacings of13 and 14 feet likewise did not satisfy the blast design criteria. Afourth iteration in the evaluation cycle for a spacing of 15 feetyielded a location for a borehole for which a compliant, cost-directedloading configuration was found. FIG. 11A provides a cross section ofthe bench at the bench and borehole and FIG. 11B illustrates thehole-to-rock face burden along the depth of the borehole. Numericalvalues for data represented in FIG. 11B are set forth in the followingTABLE.

TABLE III Hole-to- Rock Face Depth Burden 2 11.2 4 11.4 6 11.9 8 12.7 1013.8 12 13.9 14 13.6 16 13.3 18 13.0 20 12.7 22 12.4 24 12.4 26 12.7 2812.9 30 13.2 32 13.6 34 13.6 36 13.9 38 14.4 40 15.2 42 16.2 44 16.8 4617.0 48 16.8 50 16.8 52 17.1 54 17.6 56 18.2 58 18.8 60 18.8 62 19.0 6418.9 66 18.9 68 18.7 70 18.6 72 18.3 74 17.8 76 17.6 78 17.5 80 17.4 82SubDrill 82.6 SubDrill

By performing the cost-directed evaluation as described above in Example5, it was determined that with a 15 foot spacing, the segment of theborehole between the depths of 50 and 82.65 feet would not meet theblast design criteria using ANFO, so a more energetic and expensivematerial was evaluated. It was found that a thirty percent ANFO-emulsionblend was suitable for this segment in the borehole. For the segment atthe depth range of 26 feet to 50 feet, ANFO was suitable. At the depthrange of 19 to 26 feet, ANFO exceeded the energy factor criterion so theuse of stemming was indicated since there was no less energeticcandidate material under consideration. For the segment at the depthrange of 9 to 19 feet, ANFO once again met the blast design criteria.Stemming was used for the segment in the range of 0 to 9 feet, pursuantto the blast design criteria. The variable cost or materials cost forthis bore-hole was ANFO: $44.03, Thirty percent blend: $83.70; Total,$127.74. The cost per ton of rock burden associated with the hole at 15feet as described herein was about 0.28 dollars per ton and a total ofabout 1,635 tons of rock burden was associated with the borehole.

Further iterations at spacing increments of one foot produced a seriesof compliant, cost-directed loading configurations. The mostcost-effective, cost-directed loading configuration, i.e., thecost-directed spacing, occurred at a planned spacing of 27 feet. Aborehole at this position drilled to the depth of 82.65 feet with ninefeet of stemming would be filled entirely with the thirty percent blend.The resulting cost efficiency was calculated at $0.2384 per burden tonfor 2901 tons of rock burden associated with the borehole.

After holes are drilled at the cost-directed spacings, the analysisdescribed in Example 4B(ii) may optionally be performed on one or moreof the holes.

While the foregoing description refers to the use of the method ofExample 5, which makes use of a prior art method to determine rockburden, the rock burden can optionally be determined using alayer-by-layer approach like that of Example 2A or 2B for calculatingthe rock burden between the borehole and a first boundary and forsetting the second boundary so that the borehole is at the mass centerof the burden (i.e., so that the rock burden is the same on both sidesof the borehole) instead of the linear center (except in the case of afirst borehole having undefined rock burden on one side).

While the invention has been described in detail with reference toparticular embodiments thereof, it will be apparent that upon a readingand understanding of the foregoing, numerous alterations to thedescribed embodiments will occur to those skilled in the art and it isintended to include such alterations within the scope of the appendedclaims.

1. A method for choosing at least one explosive material for use in asegment of a borehole, the method comprising: determining, by aprocessor, a target specific volume energy required for an explosivematerial in the borehole; and identifying, by the processor, at leastone explosive material that provides at least the target specific volumeenergy.
 2. The method of claim 1 comprising comparing specific energiesof candidate explosive materials to the target specific volume energy.3. The method of claim 2 wherein comparing specific energies comprisesreferring to stored data that indicate specific volume energies of aplurality of explosive materials.
 4. The method of claim 3 wherein thestored data indicate the densities and specific mass energies of thevarious candidate explosive materials, and wherein identifying anexplosive material comprises calculating the specific volume energy of acandidate explosive material and comparing the candidate specific volumeenergy to the target specific volume energy.
 5. The method of claim 1,comprising partitioning the borehole into segments and determining rockburden and target specific volume energy for various segments of theborehole and separately identifying an explosive material for eachsegment.
 6. The method of claim 1 comprising determining the rock burdenfor the borehole and using a predetermined Energy Factor and the size ofthe borehole to determine the corresponding specific volume energy.
 7. Anon-transitory computer-readable medium storing code that, whenexecuted, causes a processor to: determine a target specific energyrequired for an explosive material relative to rock burden of at least asegment of a borehole; and identify at least one explosive material thatprovides at least the target specific energy.
 8. The non-transitorycomputer-readable medium of claim 7 wherein the code, when executed,causes the processor to identify said at least one explosive material byreferring to stored data indicating the specific energies of candidateexplosive materials and comparing the data to the target specificenergy.
 9. The non-transitory computer-readable medium of claim 8wherein the code, when executed, causes the processor to identify saidat least one explosive material by referring to data indicating thespecific energies of a plurality of blends of two or more materials. 10.The non-transitory computer-readable medium of claim 7 wherein the code,when executed, causes the processor to identify said at least oneexplosive material by referring to data indicating the densities andspecific mass energies of various candidate explosive materials,calculating the specific volume energy of a candidate explosivematerial, calculating the target specific volume energy and comparingthe candidate specific volume energy to the target specific volumeenergy.
 11. The non-transitory computer-readable medium of claim 7wherein the code, when executed, further causes the processor todetermine the rock burden for the borehole and determine the requiredspecific volume energy using a predetermined Energy Factor and the sizeof the borehole.
 12. The non-transitory computer-readable medium ofclaim 7 wherein the code, when executed, further causes the processor topartition the borehole into segments and determine rock burden andtarget specific volume energy for various segments of the borehole andseparately identify an explosive material for each segment.
 13. Anapparatus for choosing at least one explosive material for use in atleast one segment of a borehole having a rock burden associatedtherewith, the apparatus comprising: a computer processor; at least onecomputer-readable storage medium accessible to the processor and storingcode that, when executed, causes the processor to determine a targetspecific energy required for an explosive material relative to the rockburden and identify at least one explosive material that provides atleast the target specific energy.
 14. The method of claim 2 comprisingpartitioning the borehole into segments and determining rock burden andtarget specific volume energy for various segments of the borehole andseparately identifying an explosive material for each segment.
 15. Themethod of claim 3 comprising partitioning the borehole into segments anddetermining rock burden and target specific volume energy for varioussegments of the borehole and separately identifying an explosivematerial for each segment.
 16. The method of claim 4 comprisingpartitioning the borehole into segments and determining rock burden andtarget specific volume energy for various segments of the borehole andseparately identifying an explosive material for each segment.